Question

Seawater has density 1025 kg/m^3 and flows in a velocity field v = yi + xj, where x, y, and z are measured in meters and the components of V in meters per second. Find the rate of flow outward through the hemisphere x^2 + y^2 + z^2 = 9, z >= 0.

Answer 1

The rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.

Given that,

Seawater has a density of 1025 kg/m³ and moves at a constant velocity field defined by the equations v = yi + xj, where x, y, and z are measured in meters and the components of V are expressed in meters per second.

We have to find the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0.

We know that,

v= yi + xj, and density = 1025 kg/m³

F=1025(yi + xj)

After solving the R(u,v) we get zero.

Therefore, the rate of flow outward through the hemisphere x² + y² + z² = 9, z >= 0 is zero.

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